Interleaving: Difference between revisions
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If any maximal subword of consecutive '''Z'''s has ''q'' > 1, then the scale can be split into two subwords, ''w''<sub>1</sub> with consecutive '''Z''''s and ''w''<sub>2</sub> with consecutive non-'''Z''' letters. Consecutive non-'''Z''' letters contradict '''δ''' = '''Z''': Let ''r'' be the length of a maximal subword of non-'''Z''' letters in ''w''<sub>2</sub>. | If any maximal subword of consecutive '''Z'''s has ''q'' > 1, then the scale can be split into two subwords, ''w''<sub>1</sub> with consecutive '''Z''''s and ''w''<sub>2</sub> with consecutive non-'''Z''' letters. Consecutive non-'''Z''' letters contradict '''δ''' = '''Z''': Let ''r'' be the length of a maximal subword of non-'''Z''' letters in ''w''<sub>2</sub>. | ||
'''W'''<sub>1</sub>...'''W'''<sub>''r''</sub> (all non-'''Z'''s) | '''Z''''''W'''<sub>1</sub>...'''W'''<sub>''r''</sub>'''Z''' ('''W'''<sub>''i''</sub> are all non-'''Z'''s) | ||
(Assume WOLOG) '''W'''<sub>1</sub> + '''W'''<sub>2</sub> (in strand ''S''<sub>1</sub>) = '''Z''' + '''W'''<sub>1</sub> (in strand ''S''<sub>2</sub>) | (Assume WOLOG) '''W'''<sub>1</sub> + '''W'''<sub>2</sub> (in strand ''S''<sub>1</sub>) = '''Z''' + '''W'''<sub>1</sub> (in strand ''S''<sub>2</sub>) | ||